44 terms

Adopted from Networks, Crowds, and Markets: Reasoning about a Highly Connected World by David Easley & Jon Kleinberg

Local Clustering Coefficient

Single node focus; The probability that any two RANDOMLY selected friends of A are friends with each other.

- Ranges from Zero to 1 (when all a node's friends are friends with each other).

- Reflects how strongly TRIADIC CLOSURE is operating within the neighborhood of the node.

- The global clustering coefficient is the sum of each node's local clustering coefficient divided by two

- Ranges from Zero to 1 (when all a node's friends are friends with each other).

- Reflects how strongly TRIADIC CLOSURE is operating within the neighborhood of the node.

- The global clustering coefficient is the sum of each node's local clustering coefficient divided by two

Principle of Triadic Closure

If two people in a social network have a friend in common, then there is an increased likelihood that they will become friends themselves at some point in the future

Neighborhood Overlap

This overlap is the number of nodes who are neighbors neighbors of both A & B divided by number of nodes who are neighbors of at least one of A or B.

This is the measure of how close two nodes are to being a local bridges. This fraction is considered an "almost" ratio of becoming a local bridge.

This is the measure of how close two nodes are to being a local bridges. This fraction is considered an "almost" ratio of becoming a local bridge.

Local Bridge

When neighborhood overlap equals zero

Influence effects with Memes

Strong ties influence us more individually than collectively and Weak ties influence us more collectively more than individually. This is likely because strong tie friends are likely thinking the same thing as us anyway because of homophily. Homophily is less of an effect with weak ties so "collectively" weak ties likely bring in new ideas to influence our thinking or actions.

Reciprocal communication link

If you communicate with and other communicates back during a designated period

One-way communication link

If you sent a message to another person (note: reciprocal communication is a subset of this link set)

Maintained relationship link

If you followed information about the friend at the other end of the link, whether or not actual communication took place (e.g. clicking on Facebook's Feed service or visiting a friends profile more than once)

Order of tie strength

Weakest to Strongest tie strength

1. All Friends (may passively engaged)

2. Maintained Relationships ("following" via passive engagement)

3. One-way communication

4. Mutual communication

1. All Friends (may passively engaged)

2. Maintained Relationships ("following" via passive engagement)

3. One-way communication

4. Mutual communication

The range of Facebook users whom people actually communicate [one-way or mutual] is?

10 to 20 people

The range of Facebook users whom they follow at least passively is?

Under 50 people

Quote on the contagion of passive engagement versus mere reciprocal engagement of the past (for example, talking on the telephone).

"The stark contrast between reciprocal

and passive networks shows the effect of technologies such as News Feed. If these people were required to talk on the phone to each other, we might see something like the reciprocal network, where everyone is connected to a small number of individuals. Moving to an environment where everyone is passively engaged with each other, some event, such as a new baby or engagement can propagate very quickly through this highly connected network." -Marlow et al.

and passive networks shows the effect of technologies such as News Feed. If these people were required to talk on the phone to each other, we might see something like the reciprocal network, where everyone is connected to a small number of individuals. Moving to an environment where everyone is passively engaged with each other, some event, such as a new baby or engagement can propagate very quickly through this highly connected network." -Marlow et al.

Strong ties

These ties must be maintained; these ties require "attention", effort, and time on some continuous interval for a given period

Weak ties

Ties that need to be established at the outset but not necessarily maintained continuously

Local Bridges

Empirical studies of managers in large corporations has correlated an individual's success within a compnay to their access to ______ ______.

Embeddedness of an edge

The number of common neighbors two endpoints have; equal to the numerator of neighborhood overlap; local bridges have an embeddedness of zero.

Zero

Local Bridges have this level of embeddedness

If two individuals are connected by an embedded edge

Makes it easier for someone to trust another becasue interactions between themselves is put on "display" with a mutual friend (or many mutual friends). Group regulation and conformity to norms is likely.

Homophily Test

Less than 2gb (g=girls, b=boys); If the fraction of cross-gender edges is significantly less, then there is evidence for homophily. g and b are fractions of the sample/population that sum to one, e.g. 1/2 sample/population are boys, 1/2 sample/population are girls. So if 1/2 the edges are "cross gender" in this scenario, gender-based homophily doesn't exist (2 times 1/2 times 1/2 = 1/2)

Inverse Homophily

Greater than 2gb (p=population 1, q=population 2); If the fraction of cross gender edges is significantly more, then there is evidence of this.

g^2

Compound probability that both ends of an edge will be a girl (or some other affiliation g, e.g. race, ethnicity, age, native language, political orientation etc.

Selection

Seeking association with people who are already like you. Here, the individual characteristics drive link formation.

Social Influence

When people adapt their behaviors to become more like their friends or associates in their network. Can be viewed as the reverse of selection. Longitudinal studies of a social network can help how the social connections can affect behaviors of individuals over a period of time.

The max possible edges for n nodes can be equated by this formula

(n²-n)/2 = Total nodes n squared, minus n since nodes can't be connected to themselves, all divided by two, assuming edges are undirected. This formula is for an undirected or symmetricized network. For a directed, in-degree and out-degree network, do not divide by two, unless you're going to just measure possible in-degree edges only or just out-degree edges only.

Pascal's Triangle

The first, second and third columns of this visual diagram can be used to quickly determine the total possible edges for n when edges are symmetricized. The first column represents n. The second column represents the max edges of an n network, and the third column represents the total number of triangles generated by the network between all the nodes. Remember to double the first two columns when a net has both indegree and outdegrees, not just one type of edge.

Bipartite Graph

When a graph has two sets of nodes that connect their edges only from one set to another. Edges do not connect nodes from a single set. All edges go between the two sets. An Affiliation Network is an example of a Bipartite graph.

Interplay between selection and social influence

If two people participate in a shared focus, this provides them with an opportunity to become friends; and if two people are friends, they can influence each other's choice of foci, or the focus that he or she participates in.

Homophily

Often not an endpoint itself, but a starting part for deeper questions. Is homophily due to selection effects? Influence effects? Or is it confounding confounding effects with other diminsions that correlate with a foci e.g. like the foci of obesity may confound with people who like to eat drinks with fructose corn syrup so they intermingle more over a soda.

"Social" Affiliation Network

A network that simultaneously contains a social network on the people and an affiliation network on the people and foci. Edges in the people set connect to each other and to the foci, e.g. corporation, karate club, demographic, etc.

Difference between Triadic Closure, focal closure, and membership closure

Triadic closure is when Bob introduces Cindy to Bill.

Focal closure is when Karate introduces Anna to Daniel. Membership closure is when Anna introduces Bob to Karate.

Focal closure is when Karate introduces Anna to Daniel. Membership closure is when Anna introduces Bob to Karate.

Breadth first search

Divides a graph into layers by starting at a given node A, with all the nodes in layer d having a distance d from node A. The shortests paths from node A to a node X in layer d are precisely the paths that move downward from A to X one layer at a time.

How to compute a betweeness value for a given node A

One, perform a breadth first search of the graph, starting at Node A.

Two, determine the number of shortest pathes from A to each other node.

And three, based on these numbers, determine the amount of flow from A to all other nodes that uses each edge.

In summary, do a breadth-first to count the shortest paths from node A by moving through the layers and then determining the flow by working up from the most distant node to A

Two, determine the number of shortest pathes from A to each other node.

And three, based on these numbers, determine the amount of flow from A to all other nodes that uses each edge.

In summary, do a breadth-first to count the shortest paths from node A by moving through the layers and then determining the flow by working up from the most distant node to A

Membership Closure

The tendency of a friend to take part in an affiliation of their friend. This is a kind of social influence where another's behavior comes into closer alignment with her friends. A reason for homophily.

Focal Closure

The tendency of two people to form a social link when they have an affiliation in common. This is a form of selection where you form links to others who share characteristics with you. A reason for homophily.

Schelling Model

Shows how global patterns of spatial segregation can aris from the effect of homophily operating at a local level. Shows how segregation (or reverse homophily) can occur at the global level even when no individual seeks such a segregated outcome. Agents are assigned a threshold of how many like agents they must have adjacent edges to to feel satisfied.

Projected Graph

A people only graph derived from an affiliation graph that shows or projects just the people connected who have a common focus.

Derived Network

A people network and affiliation network combined.

Unobserved affiliation network (working in reverse)

An attempt to reconstruct and affiliation network consistent with the data. I'm assuming the number of triangles in the people graph are the minimum number of foci of affiliation...my own gut observation only.

Numerical measure of similarities

Number of foci of both A and B divided by the number of foci connected to A or B. Note this measure is similar to Neighborhood overlap and is instead, affiliation overlap.

Explanations of subtle differences of trust relationships

Trust as a result of enemy relationship or Trust as a result of Knowledge and Competence.

Characteristics of Small World networks

Clustering higher than Erdos Renyi random graphs

APL = ~4-6 hops

APL = ~4-6 hops

Rank based friendship

The proobability that a person befriends a particular candidate to the inverse of the number of closer candidates. Implies the existence of short paths under geographic routing.

A factor the rredominates the early stages of real-world message passing in one study of small world networks

Geography, then targets use non-geographic factors, like interests or profession

Greedy algorithm

Follows the problem solving heuristic of making the locally optimal choice at each stage with the hope of finding a global optimum; a greedy heuristic may yield locally optimal solutions that approximate a global optimal solution in a reasonable time